It is interesting to mention that in the expander codes of Tanner [1]}, (whose distance and decoding was later analyzed in [2]}), if the local code \(C_0\)  has rate \(\rho _0\)  then the global rate is shown to be at least \(2\rho _0-1\) . In our code the rate of the local code is \(\mbox{Rate}(C_g) = \mbox{Rate}(C_A\otimes C_B) = \rho _A\rho _B\) , and in case the graph is bipartite, we get the same bound of \(2(\rho _A\rho _B)-1\)  on the rate of the global code.
